Remark 1.1 The above examples reflect our basic perspectives about the parallel form and the mean curvature flow. (REF ) and (REF ) are some possible evidences to support these connections between them. (REF ) can be viewed as a generalization of Wang's graphical mean curvature flow ([1]}) in the curve's case. (REF ) indicates that \(\mu =\frac{1}{\Omega (T)}\)  be thought as the gradient function ([2]}) in the case of the curve shortening flow. There are no any oblivious connections between ([1]}) and ([2]}). For the curve shortening flow, however, (REF ) and (REF ) are two different forms of the same evolution equation.

